1.若數(shù)列{an}的前n項和為Sn=a^2-1（a不等于0）,則這個數(shù)列是什么數(shù)列?
a1=S1=a²-1,n=1
an=Sn-S(n-1)=(a²-1)-(a²-1)=0,n≥2
這個數(shù)列是：a²-1,0,0,0,0,……
2.等差數(shù)列{an}和{bn}的前n項和分別為Sn與Tn,對一切自然數(shù)n,都有Sn/Tn=2n/3n+1,則a5/b5等于多少?
a5/b5
=(a5+a5)/(b5+b5)
=(a1+a9)/(b1+b9)
=[(a1+a9)×9÷2]/[(b1+b9)×9÷2]
=(a1+a2+...+a9)/(b1+b2+...+b9)
=S9/T9
=(2×9)/(3×9+1)
=9/14
3.數(shù)列1又1/2,2又1/4,3又1/8,4又1/16.的前n項和為多少?
1又1/2+2又1/4+3又1/8+4又1/16+...+n又1/2^n
=(1+2+3+...+n)+(1/2+1/4++1/8+...+1/2^n)
=n(n+1)/2+(1-(1/2)^n)
=[(n²+n+2)/2]-(1/2)^n